Statistical Mechanics of Sloppy Models Bacterial CellCell Communication

Statistical Mechanics of Sloppy Models Bacterial Cell-Cell Communication and More Josh Waterfall, Jim Sethna, Steve Winans

Quorum Sensing Agrobacterium tumefaciens • Cell-cell signaling network for monitoring population density plant pathogen transfers oncogenic DNA to plant, coopting plant machinery to make nutrients. Low population density: pheromone molecule lost to environment. High density: pheromone is picked up from neighbors and signaling pathway is activated. pheromone = Quorum triggers sharing of tumor inducing plasmid

• Tra. I synthesizes small molecule (OOHL) at low, basal rate • Tra. R needs OOHL to fold properly • Active Tra. R turns on transcription of other genes, including tra. I • Hierarchically regulated by separate systems (opine and phenolic compound metabolism) Tra. R OOHL Tra. I Tra. R Tra. I Genes

26 reactions 19 chemicals 24 rate constants How to live with 24 free parameters and still make falsifiable predictions? ? ?

24 Parameter “Fit” to Data Radioactivity • Cost ≡ Energy • Also fit to six other sets of genetic and biochemical experiments (38 data points) • Still misses data 0 45 • Hand-tuning, then fancy minutes optimizations Tra. R protein is stable only with • How much can the fit OOHL parameters vary, and still fit the data? (Will give error bars)

Ensemble of Models We want to consider not just minimum cost solutions, but all solutions consistent with the available data. New level of abstraction: statistical mechanics in model space. • Huge range of scales from stiff Generate an ensemble of to sloppy : 1 inch = 103 miles states with Boltzmann • Eigendirections not aligned with weights exp(-C/T) and bare parameters compute for an observable: eigen bare O is chemical concentration, or rate constant …

Wide range of natural scales Eigenvalues – not all parameters are created equal. Range of e 20! 5 0 Log Eigenvalues -20 Sloppiness – fluctuations in eigenparameters in ensemble up to tens of orders of magnitude! Eigenparameter

Biological insight from eigenparameters Stiffest Eigenparameter Bare Parameter Stiffest eigenparameter predominantly bacterial doubling time 2 nd Stiffest Eigenparameter Bare Parameter Second stiffest adds ratio between production of Tra. R and degradation of Tra. R and OOHL

Predictions for experiments are constrained Although rate constant values are wildly undetermined, predictions for new experiments are not (always). Growth factor signaling model

Other Sloppy systems past, present, future • Growth Factor Signaling • Receptor Trafficking • Translation Dynamics • Transcription Dynamics • E-Coli Whole Cell Model • Nitrogen Cycle in Forests • Radioactive decay • Classical Potentials: Molybdenum

Acknowledgements Biology: Stephen Winans Cathy White Modeling: Jim Sethna Kevin Brown Funding: NSF ITR DOE Computational Science Graduate Fellowship